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a(n) is the least number k such that the k-th n-gonal number can be written as the difference of two positive n-gonal numbers in exactly n ways.
1

%I #6 Feb 16 2025 08:34:06

%S 5,12,82,105,297,182

%N a(n) is the least number k such that the k-th n-gonal number can be written as the difference of two positive n-gonal numbers in exactly n ways.

%C The corresponding n-gonal numbers are in A368075.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>

%e a(3) = 5: T(5) = T(6) - T(3) = T(8) - T(6) = T(15) - T(14), where T(k) is the k-th triangular number.

%Y Cf. A086270, A338105, A368041, A368075.

%K nonn,more,changed

%O 3,1

%A _Ilya Gutkovskiy_, Dec 10 2023